Consider the character of an irreducible admissible representation of a p-adic reductive group. The Harish-Chandra-Howe local expansion expresses this character near a semisimple element as a linear combination of Fourier transforms of nilpotent orbital integrals. Under mild hypotheses, we describe an explicit region on which the local character expansion is valid. We assume neither that the gr...

Andrzej Daszkiewicz and Tomasz Przebinda Department of Mathematics, N. Copernicus University, 87-100 Toruń, Poland Department of Mathematics, University of Oklahoma, Norman, OK, 73019, USA Abstract. Let e G and e G′ be a reductive dual pair of the type mentioned in the title, with e G the smaller member. Let Π and Π′ be unitary representations of e G, e G′ which occur in Howe’s correspondence. ...

Topological analysis has been performed on the total electron density of the two forms of Ozonemolecule,C2V and D3H ,to investigate the nature of chemical bonds ,molecular structure , atomiccharges and electrical properties. While these concepts have been completely discussed usingclassical models the emphasize in this work is based on Quantum Theory of Atoms in Molecules(QTAIM). Because the D3...

In this note a combinatorial character formula related to the symmetric group is generalized to an arbitrary finite Weyl group. 1 The Case of the Symmetric Group The length l(π) of a permutation π ∈ Sn is the number of inversions of π, i.e., the number of pairs (i, j) with 1 ≤ i < j ≤ n and π(i) > π(j). For any permutation π ∈ Sn let m(π) be defined as (1) m(π) := 

The pseudo-π model yields current densities and induced magnetic fields that mimic the π-component, allowing investigations of large molecular structures, whether they are planar or not, at a low computational cost but with high accuracy. Herein π-contribution to magnetically molecules nonplanar (such as [10]cyclophenacene chiral toroidal nanotubes C2016 C2196) were computed using gauge-includi...

Let F be a number field and π be an automorphic representation on GLr (AF ). In this paper we consider weighted sums of quadratic twists of the L-function for π , ∑ d L(s, π, χd ) a(s, π, d) Nd −w , where χd is a quadratic character roughly attached to F( √ d)/F . We analyze the properties which the weights a(s, π, d) must satisfy if this is to satisfy a (certain, non-abelian) group of function...